Closed geodesics in stationary manifolds with strictly convex boundary
It is known that a Lorentzian manifold with stationary metric admits at least one closed spacelike geodesic if the space section of the manifold is compact [\textit{A. Masiello}, J. Differ. Equations 104, No. 1, 48-59 (1993; Zbl 0808.53058)]. Here, the authors present a variant of that result (which in fact may be considered as an extension). They prove that a stationary Lorentzian manifold equipped with a strictly space-convex boundary admits at least one closed spacelike geodesic. The proof uses variational procedures.
scientific article; zbMATH DE number 1567208
scientific article